Comparison of Generalized Poisson and Binomial Negative Regression Models in Handling Overdispersion Based on Akaike Information Criterion
Darnah 1,*), M.Fathurahman 1), Rut Esra 1), Suyitno1), Memi Nor Hayati 1), Rahmawati Munir2)

1)Statistics Department, Faculty of Mathematics and Natural Science, Mulawarman University, Jl. Barong Tongkok No.4, kampus Gn Kelua, Samarinda, 75123
2)Physics Department, Faculty of Mathematics and Natural Science, Mulawarman University, Jl. Barong Tongkok No.4, kampus Gn Kelua, Samarinda, 75123

*Corresponding author: darnahstat[at]fmipa.unmul.ac.id

Abstract

Poisson regression analysis is the popular regression model on the discrete response variables, it has an assumption that mean and variance of response variable is equal or equidispersion. However, the count data in pulmonary tuberculosis cases often display the variance value is greater than the mean value or overdispersion. Inappropriate imposition of the Poisson regression may underestimate the standard errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This paper suggests the comparison of Generalized Poisson and Negative Binomial regression models as alternatives for handling overdispersion on pulmonary tuberculosis cases in Indonesia in 2021 based on the smallest Akaike Information Criterion (AIC) value. According to the result, AIC values of Binomial Negative regression model is smaller than the Generalized Poisson regression model. Therefore, the Binomial Negative regression model is better than Generalized Poisson regression model in handling overdispersion on the pulmonary tuberculosis cases in Indonesia in 2021.

Keywords: AIC, Binomial Negative, GPR, overdispersion, pulmonary tuberculosis cases

Topic: MATHEMATICS AND STATISTICS